We use Financial Optimum Portfolio Theory to obtain Optimum Development (Policy) Portfolios for Sub Saharan African (SSA) Countries. We estimate a model linking public expenditures on health, education and general government expenditures to the Human Development Index (HDI). Given the uncertainty of the estimated impact parameters, we obtain optimum expenditure portfolios and use them to measure the effectiveness of actual public spending. Actual HDI performance is in part due to pure chance, but significant improvements in HDI performance could be realized through the reallocation of public spending towards health and education. For some SSA countries we find that a double dividend exists, since an expansion of public expenditures may lead to both a rise in HDI performance and a fall in its corresponding variance. We also find that HDI shortfalls due to chance are uncorrelated with governance indicators, while inefficient spending and good governance are negatively correlated. Keywords Human Development Index, Public spending, Optimum Portfolio Theory